Time orientations. Dynamics is naturally expressed in terms of one-parameter groups of Jordan automorphisms \(\mathbb {R}\ni t \mapsto \mathrm {Aut(\mathcal {J}(\mathcal {A})_\mathrm {sa})}\) . Recall that for \(\mathcal {A}= \mathcal {B}(\mathcal {H}_A)\)  (in particular, for \(\mathcal {A}= M_n(\) ) every such one-parameter group is given by conjugation with a unitary or anti-unitary operator by Wigner's theorem [1]}, [2]}. In fact, Wigner's theorem holds on the level of Jordan algebras [3]}, [4]}. In \(\mathcal {A}\) , we obtain one-parameter groups of the form
\(e^{t\mathrm {ad}(ia_1)}(a_2)= e^{ita_1}a_2e^{-ita_1} \quad \quad \forall t \in \mathbb {R}, a_1,a_2 \in \mathcal {J}(\mathcal {A})_\mathrm {sa}\; .\) 
